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arXiv · 2410.06861

Vibrational resonance in the FitzHugh-Nagumo neuron model under state-dependent time delay

M. Siewe Siewe·S. Rajasekar·Mattia Coccolo·Miguel A. F. Sanjuán
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Abstract

We propose a nonlinear one-dimensional FitzHugh--Nagumo neuronal model with an asymmetric potential driven by both a high-frequency and a low-frequency signal. Our numerical analysis focuses on the influence of a state-dependent time delay on vibrational resonance and delay-induced resonance phenomena. The response amplitude at the low-frequency is explored to characterize the vibrational resonance and delay-induced resonance. By this effort, we realize that for smaller values of the amplitude of the state-dependent time-delay velocity component, vibrational resonance and multi-resonance occur in the neuronal model. For large values of the high-frequency excitation amplitude, vibrational resonance appears with one peak. We observe a decrease in the response when the amplitude of the state-dependent time-delay velocity component increases. Also, we analyze how the state-dependent time-delay position and velocity components can give birth to delay-induced resonance for separate and together. The main results of this work are that the state-dependent time-delay velocity component can play a major role in both phenomena. In fact the parameter of the delay can control the triggering of the two resonances.

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M. Siewe Siewe, S. Rajasekar, Mattia Coccolo, Miguel A. F. Sanjuán. 2024-10-09. Vibrational resonance in the FitzHugh-Nagumo neuron model under state-dependent time delay. https://arxiv.org/abs/2410.06861

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